Unit 6 Irrational Numbers and Pythagorean Theorem
Students will understand:
The meaning of the Pythagorean Theorem
The Pythagorean Theorem on the coordinate graph
Students will be able to:
Classify numbers as rational or irrational
Compare the size of irrational numbers, locate them approximately on a number line diagram, & estimate the value of expressions
Convert repeating decimals to fractions
Use square and cube roots to solve one-step equations
Draw and find the area of squares with sides of irrational length on a grid
Explain a proof of the Pythagorean Theorem
Use and apply the Pythagorean Theorem
Extend and apply the Pythagorean Theorem to solve problems in 3 dimensions
Develop and use the distance formula
Use the converse of the Pythagorean Theorem to categorize triangles
Days
Section
Lesson title/Lesson Objectives
1
Number sorting activity/Introduce rational vs irrational numbers
2
5.2
Irrational numbers (Problem 1)/Identify decimals as terminating or repeating. Convert repeating decimals to fractions.
3
Use rational approximations of irrational numbers/Compare the size of irrational numbers, locate them approximately on a number line diagram, & estimate the value of expressions
4
Square & cube roots of perfect squares & cubes/Find side length when given area and volume (multiple representations)
5
Assessment
6
Finding Squares (Park Planning as a launch)/Learn how to draw and find area of squares with sides of irrational length
7
Getting it right/Make a conjecture about the area of squares built on the sides of right triangles a2 + b2 = c2
8
Visual Proof by Transformation of Pythagorean Theorem (if time, begin using Pythagorean theorem to solve for c)
9
C6.3 & C6.5
Using the Pythagorean Theorem
10
Extending the Pythagorean Theorem to 3 Dimensions
11
C6.1 (problem 4) C6.6(problems 1-3)
Applying the Pythagorean Theorem in 2 & 3 Dimensions
12
Pythagorean Theorem on the Coordinate Graph
13
C6.4(problem 2)
Developing & Using the Distance Formula
14
Investigation: What kind of triangle?/Converse to the Pythagorean Theorem
Students will understand:
- The meaning of the Pythagorean Theorem
- The Pythagorean Theorem on the coordinate graph
Students will be able to:home